Robustness of lensless single random phase encoding systems to image sensor pixel size

In this paper, we propose a procedure to analyze lensless single random phase encoding (SRPE) systems to assess their robustness to variations in image sensor pixel size as the input signal frequency is varied. We use wave propagation to estimate the maximum pixel size to capture lensless SRPE intensity patterns such that an input signal frequency can be captured accurately. Lensless SRPE systems are contrived by placing a diffuser in front of an image sensor such that the optical field coming from an object can be modulated before its intensity signature is captured at the image sensor. Since diffuser surfaces contain very fine features, the captured intensity patterns always contain high spatial frequencies regardless of the input frequencies. Hence, a conventional Nyquist-criterion-based treatment of this problem would not give us a meaningful characterization. We propose a theoretical estimate on the upper limit of the image sensor pixel size such that the variations in the input signal are adequately captured in the sensor pixels. A numerical simulation of lensless SRPE systems using angular spectrum propagation and mutual information verifies our theoretical analysis. The simulation estimate of the sampling criterion matches very closely with our proposed theoretical estimate. We provide a closed-form estimate for the maximum sensor pixel size as a function of input frequency and system parameters such that an input signal frequency can be captured accurately, making it possible to optimize general-purpose SRPE systems. Our results show that lensless SRPE systems have a much greater robustness to sensor pixel size compared with lens based systems, which makes SRPE useful for exotic imagers when pixel size is large. To the best of our knowledge, this is the first report to investigate sampling of lensless SRPE systems as a function of input image frequency and physical parameters of the system to estimate the maximum image sensor pixel size.